# How can a quasar be 29 billion light-years away from Earth if Big Bang happened only 13.8 billion years ago? [duplicate]

I was reading through the Wikipedia article on Quasars and came across the fact that the most distant Quasar is 29 Billion Light years. This is what the article exactly says

The highest redshift quasar known (as of June 2011[update]) is ULAS-J1120+0641, with a redshift of 7.085, which corresponds to a proper distance of approximately 29 billion light-years from Earth.

Now I come to understand that the Big Bang singularity is believed to be around 13.8 Billion years ago.

So how is this possible? Does the presence of such a quasar negate the Big Bang Theory?

I'm not a student of Physics and was reading this out of (whimsical) curiosity. Is there something I'm missing here or the "proper distance" mentioned in the fact is a concept that explains this?

A simple google search led me to this article which says the farthest quasar found is 12.9 billion LYs and not 29 billion.
So in the end we have just proven that wikipedia needs more moderation.

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## marked as duplicate by Qmechanic♦May 9 '14 at 18:27

That's because the universe is expanding. The second point in my answer to this other question largely applies. – Willie Wong Jul 8 '11 at 20:19
The two sources do not contradict each other. The quasar's proper distance from us is 29 billion l.y., and light has taken 13 billion years to get to us. Here is an explanation of how that can happen: physicsforums.com/showthread.php?t=506987 – Ben Crowell Aug 8 '11 at 2:00
duplicate of physics.stackexchange.com/q/26549 – Ben Crowell Jul 11 '13 at 16:34

In the expanding universe, you have to be a bit careful to define exactly what you mean by distance. The "proper distance" referred to here in that article means the distance measured at the present time. We have to be careful even to define what we mean by that last phrase -- time is relative, you know. But if the universe is approximately homogeneous, then there is a "natural" choice of time coordinate called "cosmic time." If you imagine many, many rulers stretched out between you and the quasar, the proper distance the total length of all of them, added up at the present value of cosmic time.

That's not the same as the distance that the light has traveled, though. There are various fancy general-relativistic reasons why not, but the main idea is a very simple one. That quasar is moving away from us, so it used to be closer to us. The light we're seeing now was emitted when the distance was much shorter, so it didn't have to travel anywhere near 29 billion light-years.

The truth is that that 29-billion light-year figure is calculated based on a certain model of the universe; it's not measured directly. The model it's calculated on is based on the theory of general relativity, and includes the best currently-measured age of the universe. So pretty much by definition, there can't be any contradiction between that distance and the age of the universe.

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Yes, there is something you're missing. If you're familiar with special relativity you know that velocities don't add the same simple way they do in Newtonian mechanics. If one spaceship is moving at $c/2$ to the right and another is moving $c/2$ to the left, the relative velocity between them is not $c$, as one might expect, but $4c/5$.

In general relativity the same kind of thing applies to distances as well as velocities. In flat space we define the distance between two objects as the length of the (unique) straight line from one to the other, but in general relativity space can be curved and there is no such thing as a "straight line". The closest analog is a geodesic, which is a smoothly curved path between two points whose length is a (local) minimum. The distance to the quasar you quoted is defined as the length of a certain geodesic connecting it to us.

But there's no reason to expect geodesic distances to behave just like straight-line distances in flat space. In the FLRW metric (which defines the basic shape of the whole Universe in big bang cosmology), there exist geodesics that are longer than the geodesic from the big bang to us used to define the "age of the universe". So having a quasar whose "proper distance" or "comoving distance" from us is 29 billion light years is not a contradiction at all.

BTW, another seemingly contradictory thing you might run into is relative velocities faster than the speed of light. This can happen because relative velocity is also a tricky thing in GR, which is only defined once you decide on a specific path to "parallel transport" the velocity vector along. The relative velocity between two nearby objects is well-defined and can never be greater than $c$, but the relative velocity between two very distant objects (defined a certain way) can be greater than $c$.

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Oh, here's a great article on this topic: en.wikipedia.org/wiki/Distance_measures_%28cosmology%29 Note in particular the bottom plot, which shows that some distance measures do exceed $c$ times the age of the universe, while others do not. – Keenan Pepper Jul 8 '11 at 20:51

"Is there something I'm missing here...?"

Yes, you are missing a lot, like the fact that astronomers really don't know how far away something is, if it is more than, say, about 3k light-years out. (Compare that to the size of the our own Milky Way galaxy = 1k ly thick by 100k ly in diameter.)

Let me explain...

Our main tool for measuring how far away something that is far away is, is to use parallax: We see what direction something is from our planet, then wait half a year to take the same measurement from 2AU away. If the difference in angle is 2 arcseconds (an arcsecond is 1/3600 of a degree), then the object would have been only 1 arcsecond of difference if we could have made our second measurement from the Sun. That would mean (if you do the trigonometry) that the object is about 206265 AUs away. That's about 3.26 light-years. It is also, by definition, a parsec (short for "parallax of an arc-second").

Even though 1 arcsecond is an eensy-weensy-itty-bitty-very-super-tiny-small angle, we have the equipment to accurately measure it. Nailing down Alpha Centauri, at about 4 light-years (just over a parsec) away, for instance, is a piece of cake. But as you go farther out, it gets harder. Judging the distance of an object by parallax that is 400 light-years away, for instance, would take equipment and methods which are one hundred times more accurate than those which could barely peg Alpha Centauri. Judging the actual distance of objects at 4000 light-years takes a thousand-fold increase in accuracy.

The bottom line is that at a certain point we can't tell jack using parallax. We lose 3-D vision of the stars, and everything looks like it was painted on a great curved canvas. The distance at which this happens is close enough that the vast majority of our own galaxy appears in 2-D. Certainly any other galaxy is way, WAY beyond the point where 3-D viewing becomes impossible.

So how do we tell how far away stuff is? We guess. Astrononers say, "Hmmm, that star has a color of 'this', and we think it's color should be 'that', and 'this' minus 'that' is the red shift. And a red shift of 'that' means it must be moving away at this speed. And our theory says the universe is this old; so (guesstimated speed) x (theoretical time) means it must be this far away.

So, when someone tells you that something is 29 BILLION light-years away, and you know we start guessing in the 100s or 1000s of light-years, then you KNOW they are flat out pulling a WAG out of their nether-regions.

If that doesn't knock your socks off, this might:

Not too long ago, one of these bright, telescope-toting homosapiens realized that the red shift from all these galaxies indicated an initial starting point for the universe which was, galactically speaking, very, very, Very, VERY close to our neck of the Milky Way. That was absolutely unacceptable, since it might fuel a creationist view of things. So a theory was invented that EVERYTHING was expanding: the space between galaxies, the space within galaxies, even the space between the atoms in your body. Then someone realized that doesn't quite hold water. Don't know where this theory has morphed to in recent years, as I do not try to track fairytales in the birthing process, but I await, with bemusement, the tortured death of it and the move to something even more insane.

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Who is this "someone" that realized something "doesn't quite hold water"? And what specifically doesn't hold water: general relativity, big bang cosmology, or just the FLRW metric? There's pretty strong consensus in the scientific community for all those things... – Keenan Pepper Jul 8 '11 at 20:30
-1, This ignores so much. First, parallax was used to calibrate things like the main sequence brightness/color relationship and the luminosity/frequency relationship of the Cepheid variable stars. This alone is enough to show that the Andromeda galaxy is around 2.5 million light years (with small error bars!) away, and falsify your 2-3 Kly hypothesis. Further distances are determined by using these indicators to calibrate the brightness of type IIa supernovae, and that is used to calculate Hubble's constant, which generates the final estimate. – Dan Jul 8 '11 at 21:16
@Keenan, specifically the theory that everything is blowing up. That your head, my head, everyone's head (and the rest of us and the rest of the Earth and the rest of space) is expanding at a rate rapid enough to induce significant red shift in most of the universe we see. That is specifically what I am saying that some scientists are saying doesn't hold water. Maybe your head is expanding at an incredible rate but.. hold on, checking... yep... mine still is the same size... maybe shrinking a little.. – Vintage Jul 11 '11 at 19:49
@Vintage Your comments indicate that you don't really understand the theory that you're disputing. Big bang cosmology does not predict that anyone's head is expanding, nor even larger things like stars or galaxies. See physics.stackexchange.com/q/2110 – Keenan Pepper Jul 12 '11 at 5:17
I think it is worth noting that the so called "ladder of distance" that is used to establish these things theses days has multiple paths which support and cross-check each other. Perhaps we should start calling it the "scaffold of distance". – dmckee Oct 4 '14 at 17:13